H2 Physics Thermodynamics Notes: First Law, p-V Work, Heat Capacity | 9478

Q: What should I revise for H2 Physics thermodynamic systems?
A: For SEAB 9478 Topic 13, revise internal energy, thermal equilibrium, work done by and on a gas, the zeroth law, the First Law (\Delta U=Q+W), specific heat capacity, and specific latent heat.

TL;DR
Thermodynamics is the energy accounting chapter. Nail the distinctions between U, Q, W, then gas laws, kinetic theory, p-V graphs, and calorimetry questions become much easier to organise.

Concrete example: how to use this page

For a gas in a cylinder, ask three questions: did heat enter, did the gas do work, and did internal energy change? Answer those before substituting into the First Law.

First Law decision map

Misconception check: Heat is not stored inside a system. Heating is an energy transfer across the boundary; internal energy is the store that changes after heating and work have been accounted for.

If you searched for thermal physics notes

Stay synced with the adjacent thermal-physics chapters via the H2 Physics notes hub; it bundles Temperature and Ideal Gases plus the rest of the 9478 sequence.

1 Internal energy $(U)$

The macroscopic state of a system fixes its internal energy: the sum of random microscopic kinetic $(E_k)$ and potential $(E_p)$ energies. No single thermometer can reveal $U$ directly - you must track how energy enters or leaves.

1.1 Parent takeaway

A student who writes “heat stored in the gas” is forfeiting method marks. Heat is a transfer, not a store.

1.2 Mini-drill

State whether each contributes to $U$:

2 Thermodynamic temperature $(T)$

Absolute temperature in kelvin is directly proportional to the mean kinetic energy per particle. Doubling $T$ doubles $\langle E_k \rangle$. Always quote exam answers to 2-3 s.f. unless otherwise stated.

3 Heating $(Q)$ vs work $(W)$

Sign hack: This page uses (W) as work done on the system. Work done by the gas therefore has the opposite sign in (\Delta U = Q + W).

4 Zeroth law - the thermometer principle

If A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C. This justifies using a third body (a thermometer) to compare temperatures.

5 First law - the energy ledger

$$\Delta U = Q + W.$$

1. Positive $Q$: heating adds energy.
2. Positive $W$: surroundings compress system.
3. For an ideal gas in free expansion, $Q = 0$ and $W = 0$, hence $\Delta U = 0$

First Law sign checkpoint

Before substituting into $\Delta U = Q + W$, translate the wording into this note's convention: $W$ is positive when work is done on the system.

Misconception check: "work done by the gas" and "work done on the gas" have opposite signs. If you calculate work by the gas as $p\Delta V$, convert it to work on the gas by changing the sign before using this First Law form.

Process constraint checkpoint

After setting the sign convention, identify the process constraint before doing arithmetic. The constraint usually tells you which First Law term is zero or which state variable stays fixed.

Worked check: in an insulated compression, $Q=0$. If the surroundings do $\pu{250 J}$ of work on the gas, then $\Delta U = +\pu{250 J}$, so the gas temperature rises for an ideal gas.

Misconception check: "constant" does not always mean "zero". Constant volume gives zero work; constant temperature gives zero internal-energy change for an ideal gas; constant pressure can still involve work.

p-V area checkpoint

On a p-V diagram, the area under the path gives the work done by the gas during a volume change. Convert that area into this note's First Law sign convention before substituting into $\Delta U = Q + W$.

Worked check: a gas expands at constant pressure $\pu{120 kPa}$ from $\pu{1.0 L}$ to $\pu{3.5 L}$. The area is $120(3.5-1.0)=\pu{300 J}$

Misconception check: the p-V area does not automatically have the sign used in every textbook convention. First decide whether it is work by the gas or work on the gas, then match the convention used in the equation.

6 Specific heat capacity $(c)$

Defined as the heat required per unit mass per kelvin rise:

$$Q = mc \Delta T.$$

6.1 Quick-check

Water has $c \approx 4.18 \space \pu{kJ.kg-1.K-1}$ - roughly 11x that of copper ($\approx 0.39 \space \pu{kJ.kg-1.K-1}$

7 Specific latent heat $(L)$

Energy per unit mass for a phase change at constant $T$:

$$Q = mL.$$

Common values:\

8 WA & Paper 4 timing rules

1. Use the official paper durations and marks as a pacing guide: Papers 2 and 3 average about 1.6 min/mark, while Paper 4 averages about 3 min/mark.
2. Copy units first when using data-book tables.
3. Show full working so the energy-transfer setup, sign convention, and unit conversions remain visible.

Need structured practice on Thermodynamic Systems? Our H2 Physics tuition programme covers this topic with weekly problem sets and practical data-handling drills.

Comprehensive revision pack

9478 Section IV, Topic 13 Syllabus outcomes

Candidates should be able to:

• (a) show an understanding that the macroscopic state of a system determines the internal energy of the system, and that internal energy can be expressed as the sum of a random distribution of microscopic kinetic and potential energies associated with the particles of the system.
• (b) show an understanding that the thermodynamic temperature of a system is (directly) proportional to the mean microscopic kinetic energy of particles.
• (c) show an understanding that when two systems are placed in thermal contact, energy is transferred (by heating) from the system at higher temperature to the system at lower temperature, until they reach the same temperature and achieve thermal equilibrium (i.e. no net energy transfer).
• (d) show an understanding of the difference between the work done by a gas and the work done on a gas, and calculate the work done by a gas in expanding against a constant external pressure: $W = p\Delta V$.
• (e) recall and apply the zeroth law of thermodynamics that if two systems are both in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.
• (f) recall and apply the first law of thermodynamics, $\Delta U = Q + W$

Concept map (in words)

Identify the process path (constant T, V, p or adiabatic). Track energy transfers: heating (Q) and work (W) alter internal energy (U). Use c and L for temperature changes and phase changes respectively. p-V diagrams visualise work as area under curve.

Key relations

Derivations & reasoning to master

1. First law sign convention: derive for compression and expansion, then state whether each work term is work done by the gas or work done on the gas.
2. Work on a p-V diagram: show $W = \int p \space \mathrm{d}V$ and interpret the area under the curve.
3. Heating vs temperature change: explain why adding latent heat occurs without temperature change.
4. Adiabatic vs isothermal: compare outcomes for $\Delta U$ to emphasise physical differences.

Worked example 1 - heating and work

An ideal gas is compressed slowly from $\pu{4.0 L}$ to $\pu{2.0 L}$ at constant pressure $\pu{150 kPa}$ while $\pu{1.6 kJ}$ of heat is removed. Find the change in internal energy.

Method: $W = -p \Delta V$ (constant $p$); apply $\Delta U = Q + W$. Discuss the sign of $\Delta U$

$$\Delta V = 2.0 - 4.0 = -2.0\,\pu{L} \Rightarrow W = -p\Delta V = -150(-2.0)=+300\,\pu{J}=\pu{0.30 kJ}.$$

Heat is removed so $Q=-\pu{1.6 kJ}$. Hence

$$\Delta U = Q + W = (-1.6 + 0.30)\,\pu{kJ} = -\pu{1.3 kJ}.$$

Worked example 2 - latent heat application

$\pu{0.45 kg}$ of ice at $\pu{-12 ^\circ C}$ is heated to steam at $\pu{110 ^\circ C}$. Calculate the total energy required. Use $c_{\text{ice}}$

Approach: break into stages: warm ice → melt → warm water → vaporise → superheat steam. Sum each $Q$.

Using typical data-book values $c_{\text{ice}}\approx \pu{2.1 kJ.kg-1.K-1}$

$$Q \approx 0.45\left[2.1(12) + 334 + 4.18(100) + 2260 + 2.0(10)\right]\,\pu{kJ} \approx \pu{1.38 MJ}.$$

Practical & data tasks

• Plot p-V data from a piston experiment using dataloggers; estimate work via trapezium rule.
• Carry out a calorimetry experiment to determine specific heat of an unknown metal; include uncertainty analysis.
• Observe a pressure cooker in operation; relate pressure increase to boiling point shift using phase diagrams.

Common misconceptions & exam traps

• Saying “heat stored in the gas” instead of internal energy increases.
• Confusing sign convention for work (especially in expansion scenarios).
• Neglecting to convert kPa·L to joules $\pu{1 kPa \cdot L} = \pu{1 J}$.
• Forgetting to include phase-change energy when warming substances across melting or boiling points.

Quick self-check quiz

1. In an isothermal expansion of an ideal gas, what is $\Delta U$? - Zero.
2. What does a horizontal line on a heating curve represent? - Phase change at constant temperature (latent heat).
3. State the first law of thermodynamics. - $\Delta U = Q + W$.
4. Does compressing a gas adiabatically increase or decrease its temperature? - Increase (internal energy rises).
5. Which process has zero work: isochoric or isobaric? - Isochoric (volume constant).

Revision workflow

1. Re-draw schematic p-V diagrams for each thermodynamic process and label $Q$, $W$, $\Delta U$ signs.
2. Practise energy accounting problems mixing Q and W until you can do them without hesitation.
3. Build a table of specific heats and latent heats for common materials (water, ice, steam, metals).
4. Solve past-paper calorimetry questions and compare marking scheme language to adopt proper phrasing.

Practice Quiz

Test yourself on the key concepts from this guide.

9 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Internal Energy - Wikipedia
• Kinetic Theory & Temperature - LibreTexts

10 Call-to-action

Parents: schedule a 1-hour Thermodynamic Systems clinic two weeks before WA 2. Students: print the First Law equation and stick it on your water bottle - then apply it to every past-year Qn you meet.

Last updated 14 Jul 2025. Next review when SEAB publishes a newer H2 Physics syllabus document.